Answer:
Yes, between 0.84 seconds and 0.85 seconds after the shot is launched.
Step-by-step explanation:
[tex]\text{The equation for ball height} : 6+30\cdot t-16\cdot t^{2}\\\text{The equation for shot blocker's height} : 9+25\cdot t-16\cdot t^{2}[/tex]
But, the shot is made before two tenths of a second or 0.2 seconds therefore modified equation for ball height is :
[tex]6+30\cdot (t-0.2)-16\cdot (t-0.2)^{2}[/tex]
Now for the shot to be blocked,the height of shot blocker must be greater than the height of the ball which is shot before 0.2 seconds :
[tex]\implies 9+25\cdot t-16\cdot t^{2}\geq 6+30\cdot (t-0.2)-16\cdot (t-0.2)^{2}\\\implies 9+25\cdot t-16\cdot t^{2}\geq 6+30\cdot t-6-16\cdot (t^{2}-0.4\cdot t+0.04)\\\implies9+25\cdot t-16\cdot t^{2}\geq 30\cdot t-16\cdot t^{2}+6.4\cdot t-0.64\\\implies 9+25\cdot t\geq 36.4\cdot t-0.64\\\implies 9.64\geq 11.4\cdot t\\\\\implies t\leq \frac{9.64}{11.4}\approx 0.846[/tex]
Hence, the shot was blocked between 0.84 and 0.85 seconds after the shot is launched.
